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5.3 part 3 – Solving
Quadratic Equations by
Factoring
Objective: TSW solve quadratic equations
by factoring.
Answers to Homework 1. (x+6)(x-6) 10. (3x+7)(x-1)
2. (7x-4)(7x+4) 11. (x+5)(2x+3)
3. (5c-b)(5c+b) 12. (3x+4)(3x-2)
4. (2x2 – 9y)(2x2 +9y) 13. (2x-7)(x+2)
5. 3(x-3)(x+3) 14. (4y + 1)(3y + 1)
6. 2(x-1)(x+1) 15. (x+5)(2x-1)
7. (x-1)(7x-4) 16. (2x+3)(x+2)
8. (n+3)(5n+2) 17. (4a-3)(2a-1)
9. (2y+3)(2y+1) 18. (y-4)(2y+5)
To Solve a Quadratic Equation by Factoring:
1. Put the equation in standard form AND
Factor the equation completely.
2. Set each factor equal to zero.
• Zero Product Property – where you can set
each factor equal to zero.
• A factor is ANYTHING with an x in it
3. Solve for x (Which are the values where
the parabola crosses the x-axis)
4. Check Solutions
Examples: Solve each equation by factoring:
1. f(x) = -2x2 + 11x
Let’s factor – GCF is -x, so:
0 = -x(2x – 11)
Each item which has an x is set equal to zero:
-x = 0 2x – 11 = 0
-1 -1 + 11 +11
x = 0 2x = 11
2 2
x = 0, 11
2
2. x2 – 14x = -45
+45 +45
x2 – 14x + 45 = 0
Now let’s factor:
No GCF, so what multiplies to (a·c = 45)
and adds to (b=-14)?
-9 and -5
(x – 9)(x – 5)=0
x – 9 = 0 x – 5 = 0
+9 +9 + 5 +5
x = 9 x = 5
3. h(x) = 25x2 – 16
0 = 25x2 – 16
It’s a difference of two perfect squares:
0 = (5x – 4)(5x + 4)
Set each factor equal to zero.
5x – 4 = 0 5x + 4 = 0
+4 +4 - 4 -4
5x = 4 5x = -4
5 5 5 5
x = 4, -4
5 5
4. g(x) = 3x2 + 12x
GCF is 3x, so:
g(x) = 3x(x + 4)
0 = 3x(x + 4)
Set each factor equal to zero:
3x = 0 x + 4 = 0
3 3 - 4 -4
x = 0 x = -4
x = 0, -4
5. 4x2 + 1 = 4x
Standard form: 4x2 – 4x + 1 = 0
No GCF, so what two numbers multiply to (a·c = 4) and add to (b = -4)?
-2 and -2
(x – 2)(x – 2)
Since a=4, we MUST use Bottom’s Up
(x – 2)(x – 2)
4 4
(x - ½)(x - ½)
(2x – 1)(2x – 1)
2 x – 1 = 0 2x – 1 = 0
+ 1 +1 + 1 +1
2x = 1 2x = 1
2 2 2 2
x = ½ x = ½
6. 5x2 – 5x = 30
5x2 – 5x – 30 = 0
GCF is 5, so:
5(x2 – x – 6)
What multiplies to (a·c = -6) and adds to
(b = -1)?
-3 and 2
5(x – 3)(x + 2) = 0, only items with an x we set equal to zero, so:
x – 3 = 0 x + 2 = 0
+3 +3 - 2 -2
x = 3 x = -2
A parabola is
even found
on this lovely
smiley face
HAVE A NICE TURKEY DAY!
Homework
5.3 part 3 page 272 #’s 13-15, 38-43, 59,60